Problem: Emily is 15 years younger than Ashley. Twelve years ago, Ashley was 4 times older than Emily. How old is Ashley now?
Solution: We can use the given information to write down two equations that describe the ages of Ashley and Emily. Let Ashley's current age be $a$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $a = e + 15$ Twelve years ago, Ashley was $a - 12$ years old, and Emily was $e - 12$ years old. The information in the second sentence can be expressed in the following equation: $a - 12 = 4(e - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to solve our first equation for $e$ and substitute it into our second equation. Solving our first equation for $e$ , we get: $e = a - 15$ . Substituting this into our second equation, we get the equation: $a - 12 = 4($ $(a - 15)$ $ -$ $ 12)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $a - 12 = 4a - 108$ Solving for $a$ , we get: $3 a = 96$ $a = 32$.